From Middle Market to BB/EB

Hi all,

I recently secured an internship at an M&A boutique in London. Not a big name but decent deal activity and good coverage.

This will be my first internship in banking, and my aim would be to work in a BB or EB boutique in the future.

Is this kind of transition from MM specialist to BB/EB something that happens a lot or should I just aim to stay in middle-market?
Also is there a kind of snobbism against MM bankers just like there is one for big 4 audit TS ?

Thanks!